Is (−2,2)

Question

a viable solution for the following system? Explain.

−7x+2y=18

3x+3y=0

(1 point)
Responses

(−2,2)
is a viable solution since it makes one equation true.
left parenthesis negative 2 comma 2 right parenthesis is a viable solution since it makes one equation true.

(−2,2)
is a nonviable solution since it makes one equation true.
left parenthesis negative 2 comma 2 right parenthesis is a nonviable solution since it makes one equation true.

(−2,2)
is a nonviable solution since it makes neither equation true.
left parenthesis negative 2 comma 2 right parenthesis is a nonviable solution since it makes neither equation true.

(−2,2)
is a viable solution since it makes both equations true.

Answer 1

To determine if the point \((-2, 2)\) is a viable solution for the system of equations, we need to substitute \(x = -2\) and \(y = 2\) into both equations and check if the equations hold true.

1. First equation: \[ -7x + 2y = 18 \] Substitute \(x = -2\) and \(y = 2\): \[ -7(-2) + 2(2) = 14 + 4 = 18 \] This is true, as both sides equal \(18\).

2. Second equation: \[ 3x + 3y = 0 \] Substitute \(x = -2\) and \(y = 2\): \[ 3(-2) + 3(2) = -6 + 6 = 0 \] This is also true, as both sides equal \(0\).

Since the point \((-2, 2)\) satisfies both equations, it is a viable solution.

The correct response is: \((-2,2)\) is a viable solution since it makes both equations true.

Answer 2

The sum of twice the number of green marbles and the number of yellow marbles in a bag is more than 20. The total number of green and yellow marbles is less than 15. Which of the following is a viable solution to the system of inequalities, where x is the number of green marbles and y is the number of yellow marbles?(1 point)
Responses

(3,12)
left parenthesis 3 comma 12 right parenthesis

(8,6)
left parenthesis 8 comma 6 right parenthesis

(10,5)
left parenthesis 10 comma 5 right parenthesis

(6,7)

Answer 3

To determine which of the given points \((x, y)\) is a viable solution to the system of inequalities, we first need to define the inequalities based on the problem statement:

1. The sum of twice the number of green marbles and the number of yellow marbles is more than 20: \[ 2x + y > 20 \]

2. The total number of green and yellow marbles is less than 15: \[ x + y < 15 \]

Now, we will evaluate each option to see if they satisfy both inequalities.

Option 1: (3, 12)

1. Check \(2x + y > 20\): \[ 2(3) + 12 = 6 + 12 = 18 \quad (\text{not } > 20) \]

2. Check \(x + y < 15\): \[ 3 + 12 = 15 \quad (\text{not } < 15) \]

Conclusion: \((3, 12)\) is not a viable solution.

Option 2: (8, 6)

1. Check \(2x + y > 20\): \[ 2(8) + 6 = 16 + 6 = 22 \quad (> 20) \]

2. Check \(x + y < 15\): \[ 8 + 6 = 14 \quad (< 15) \]

Conclusion: \((8, 6)\) is a viable solution.

Option 3: (10, 5)

1. Check \(2x + y > 20\): \[ 2(10) + 5 = 20 + 5 = 25 \quad (> 20) \]

2. Check \(x + y < 15\): \[ 10 + 5 = 15 \quad (\text{not } < 15) \]

Conclusion: \((10, 5)\) is not a viable solution.

Option 4: (6, 7)

1. Check \(2x + y > 20\): \[ 2(6) + 7 = 12 + 7 = 19 \quad (\text{not } > 20) \]

2. Check \(x + y < 15\): \[ 6 + 7 = 13 \quad (< 15) \]

Conclusion: \((6, 7)\) is not a viable solution.

Final Conclusion

The only viable solution to the system of inequalities is \((8, 6)\).